Solving Nonlinear Second-Order ODEs via the Eisenhart Lift and Linearization

Author:

Paliathanasis Andronikos12ORCID

Affiliation:

1. Institute of Systems Science, Durban University of Technology, P.O. Box 1334, Durban 4000, South Africa

2. Departamento de Matemáticas, Universidad Católica del Norte, Avda. Angamos 0610, Casilla 1280, Antofagasta 1270709, Chile

Abstract

The linearization of nonlinear differential equations represents a robust approach to solution derivation, typically achieved through Lie symmetry analysis. This study adopts a geometric methodology grounded in the Eisenhart lift, revealing transformative techniques that linearize a set of second-order ordinary differential equations. The research underscores the effectiveness of this geometric approach in the linearization of a class of Newtonian systems that cannot be linearized through symmetry analysis.

Publisher

MDPI AG

Reference54 articles.

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